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# x is a negative integer

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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x is a negative integer [#permalink]  26 Jan 2016, 01:17
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Question Stats:

69% (00:49) correct 30% (00:34) wrong based on 53 sessions
x is a negative integer.

 Quantity A Quantity B $$2^x$$ $$3^{x+1}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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Question: 5
Page: 466
Difficulty: medium
[Reveal] Spoiler: OA

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 112

Kudos [?]: 1865 [1] , given: 397

Re: x is a negative integer [#permalink]  26 Jan 2016, 01:59
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Solution

Since both quantities are algebraic expressions, another way to approach the comparison is to set up a placeholder relationship, denoted by |?|, between the two quantities and then to simplify to see what conclusions you can draw. As you simplify and draw conclusions, keeping in mind that x is a negative integer.

$$2^x |?| 3^x^+^1$$

or $$2^x |?| 3* 3^x$$
or $$\frac{2^x}{3^x} |?| 3$$

Let n = -x and since x is negative integer n is a positive integer.

or $$(\frac{2}{3})^{-n} |?| 3$$

or $$(\frac{3}{2})^n |?| 3$$

Now clearly for some values of n Quantity A is bigger (for example n = 1) and other values Quantity B is greater (for example n=3). Hence a relation ship between the two cannot be determined. Option D is correct.
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Re: x is a negative integer [#permalink]  26 Jan 2016, 14:05
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sandy wrote:
x is a negative integer.

 Quantity A Quantity B $$2^x$$ $$3^x^+^1$$

Let's test some values of x.

x = -1
Quantity A = 2^(-1) = 1/2
Quantity B = 3^(-1 + 1) = 3^0 = 1
In this case, quantity B is greater

x = -3
Quantity A = 2^(-3) = 1/8
Quantity B = 3^(-3 + 1) = 3^(-2) = 1/9
In this case, quantity A is greater

Answer: D

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Brent
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Re: x is a negative integer [#permalink]  09 Jun 2017, 14:36
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Not edited properly mate.

It should be $$3^{x+1}$$ not $$3^x$$ + 1

Made me choose the wrong option.

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Re: x is a negative integer [#permalink]  11 Jun 2017, 09:53
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sandy wrote:
x is a negative integer.

 Quantity A Quantity B $$2^x$$ $$3^x^+^1$$

Let's plug in some values for x and see what happens

x = -1
We get:
Quantity A: 2^(-1) = 1/2
Quantity B: 3^(-1 + 1) = 3^0 = 1
Quantity B is greater

x = -3
We get:
Quantity A: 2^(-3) = 1/8
Quantity B: 3^(-3 + 1) = 3^(-2) = 1/9
Quantity A is greater

Answer:
[Reveal] Spoiler:
D

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Re: x is a negative integer [#permalink]  29 Nov 2018, 15:02
Can someone please tell me why 3^x+1 is the same as 3∗3^x?

Or can just tell me the name of the rule?

I'm sure I should know it, but I don't.

Thanks for your help.
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Re: x is a negative integer [#permalink]  29 Nov 2018, 17:14
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arc601 wrote:
Can someone please tell me why 3^x+1 is the same as 3∗3^x?

Or can just tell me the name of the rule?

I'm sure I should know it, but I don't.

Thanks for your help.

It's called the Product Law, which says (b^x)(b^y) = b^(x + y)
For example, (2^5)(2^3) = 2^(5 + 3) = 2^8

So, (3)(3^x) = (3^1)(3^x)
= 3^(1 + x)
= 3^(x + 1)

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Re: x is a negative integer   [#permalink] 29 Nov 2018, 17:14
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# x is a negative integer

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